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Simplifying 5x2 + -33x + -10 = 0 Reorder the terms: -10 + -33x + 5x2 = 0 Solving -10 + -33x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2 + -6.6x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -6.6x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -6.6x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -6.6x + x2 = 0 + 2 -6.6x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -6.6x + x2 = 2 The x term is -6.6x. Take half its coefficient (-3.3). Square it (10.89) and add it to both sides. Add '10.89' to each side of the equation. -6.6x + 10.89 + x2 = 2 + 10.89 Reorder the terms: 10.89 + -6.6x + x2 = 2 + 10.89 Combine like terms: 2 + 10.89 = 12.89 10.89 + -6.6x + x2 = 12.89 Factor a perfect square on the left side: (x + -3.3)(x + -3.3) = 12.89 Calculate the square root of the right side: 3.590264614 Break this problem into two subproblems by setting (x + -3.3) equal to 3.590264614 and -3.590264614.Subproblem 1
x + -3.3 = 3.590264614 Simplifying x + -3.3 = 3.590264614 Reorder the terms: -3.3 + x = 3.590264614 Solving -3.3 + x = 3.590264614 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.3' to each side of the equation. -3.3 + 3.3 + x = 3.590264614 + 3.3 Combine like terms: -3.3 + 3.3 = 0.0 0.0 + x = 3.590264614 + 3.3 x = 3.590264614 + 3.3 Combine like terms: 3.590264614 + 3.3 = 6.890264614 x = 6.890264614 Simplifying x = 6.890264614Subproblem 2
x + -3.3 = -3.590264614 Simplifying x + -3.3 = -3.590264614 Reorder the terms: -3.3 + x = -3.590264614 Solving -3.3 + x = -3.590264614 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.3' to each side of the equation. -3.3 + 3.3 + x = -3.590264614 + 3.3 Combine like terms: -3.3 + 3.3 = 0.0 0.0 + x = -3.590264614 + 3.3 x = -3.590264614 + 3.3 Combine like terms: -3.590264614 + 3.3 = -0.290264614 x = -0.290264614 Simplifying x = -0.290264614Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.890264614, -0.290264614}
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